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Three letters are written to different persons and addresses on three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope, is
- a)1/6
- b)1/28
- c)1/27
- d)1/9
Correct answer is option 'A'. Can you explain this answer?
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Three letters are written to different persons and addresses on three ...
Solution:
Let us assume that the three letters are A, B, and C and the three envelopes are numbered 1, 2, and 3.
Total possible ways of arranging these letters in envelopes are 3! = 6.
Let us consider the case where all the letters are in the wrong envelope.
Letter A can go into envelopes 2 or 3 (2 ways).
Letter B can go into the remaining envelopes (1 way).
Letter C can go into the remaining envelope (1 way).
Thus, there is only 1 way in which all three letters are in the wrong envelopes.
Therefore, the probability that the letters go into the right envelopes is (total possible ways - only 1 way) / total possible ways = 5/6.
But we are asked to find the probability without looking at the addresses, which means we are assuming that the arrangement of the letters in the envelopes is completely random.
In this case, the probability of each arrangement is equally likely.
Out of the 6 possible arrangements, only 1 arrangement is correct.
Therefore, the probability that the letters go into the right envelopes is 1/6.
Hence, the correct option is (a) 1/6.
Let us assume that the three letters are A, B, and C and the three envelopes are numbered 1, 2, and 3.
Total possible ways of arranging these letters in envelopes are 3! = 6.
Let us consider the case where all the letters are in the wrong envelope.
Letter A can go into envelopes 2 or 3 (2 ways).
Letter B can go into the remaining envelopes (1 way).
Letter C can go into the remaining envelope (1 way).
Thus, there is only 1 way in which all three letters are in the wrong envelopes.
Therefore, the probability that the letters go into the right envelopes is (total possible ways - only 1 way) / total possible ways = 5/6.
But we are asked to find the probability without looking at the addresses, which means we are assuming that the arrangement of the letters in the envelopes is completely random.
In this case, the probability of each arrangement is equally likely.
Out of the 6 possible arrangements, only 1 arrangement is correct.
Therefore, the probability that the letters go into the right envelopes is 1/6.
Hence, the correct option is (a) 1/6.
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Three letters are written to different persons and addresses on three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope, isa)1/6b)1/28c)1/27d)1/9Correct answer is option 'A'. Can you explain this answer?
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